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4 years ago

Which point could be on the line that is perpendicular to and passes through point K?

Mathematics

2 answers:

Ede4ka [16]4 years ago

3 0

It would be (2,2), because of the opposite reciprocal slope of a perpendicular line.

LUCKY_DIMON [66]4 years ago

3 0

Answer:

(2, 2)

Step-by-step explanation:

First we find the slope of the line through M and N. The coordinates of M are (2, 3) and the coordinates of N are (-3, 2). Using the formula for slope,

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-2}{2--3}=\frac{1}{5}$

For a line to be perpendicular to a given line, the slopes would be negative reciprocals (opposite signs and the fraction is flipped). This makes the slope of the perpendicular line -5/1.

The coordinates of point K are (3, -3). Going down 5 units and right 1 unit would put it at (4, -8). Going backwards, up 5 units and left 1 unit would be (2, 2). Thus (2, 2) is the point we are looking for.

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Find the equation of the directrix of the parabola found in part A.

elena-s [515]

The specific equation of the parabola can be found by plugging the given

values of the variables of the general equation.

<h3>Correct Response;</h3>

$\displaystyle The \ equation \ of \ the \ parabolic \ reflector \ is; \ \underline{ y = \frac{1}{12} \cdot x^2}$

<h3>Method used to obtain the above equation;</h3><h3 /><h3>Given parameters;</h3>

The vertex of the parabola is at the origin with coordinates (0, 0)

The location of the focus = 3 cm from the vertex

<h3>Required:</h3>

The equation that models the parabola.

<h3>Solution:</h3>

The vertex form of the equation of a parabola is y = a·(x - h)² + k

The above equation can be expressed as (x - h)² = 4·p·(y - k)

Where in a vertical parabola;

(h + p, k) = The coordinates of the focus

(h, k) = The coordinates of the vertex = (0, 0)

p = 3 = The distance of the focus from the vertex

Therefore, the coordinates of the focus = (0 + 3, 0) = (3, 0)

The equation of the parabola is therefore;

(x - 0)² = 4×3 × (y - 0) = 12·y

x² = 12·y

$\displaystyle The \ equation \ of \ the \ parabola \ that \ models \ the \ reflector \ is; \ \underline{ y = \frac{1}{12} \cdot x^2}$

Learn more about the equation of a parabola here:

brainly.com/question/2131669

5 0

3 years ago

How many solutions does the equation have??<br> 3(d+11)=6(d+33) PLEASE HELP MEEEEEEE

Misha Larkins [42]

A powerful way to find out is to solve the equation. Let's try that.

   3 (d + 11) = 6 (d + 33)

Eliminate the parentheses: 3d + 33 = 6d + 198

Subtract 3d from each side: 33 = 3d + 198

Subtract 198 from each side: -165 = 3d

Divide each side by 3 : - 55 = d

There it is ... the solution to the original equation.
'd' has to be -55, otherwise the original equation isn't a true statement.
-55 is the ONLY number that 'd' can be. If you write in any other number
for 'd', the equation will be false.

For example, less see what the equation says when d=2 :

   3(2 + 11) = 6(2 + 33)

   3( 13 ) = 6( 35 )

   39    = 210

Is that a true statement ? Is 39 equal to 210 ?
No. 39 and 210 are not equal. They are different.
So the equation is not true when d = 2 .
The equation is true ONLY when d = -55 .

The equation has exactly one solution.

4 0

3 years ago

1/2 of a bowl of cereal is divided equally between 4 bowls. how much cereal is in each bowl

Lubov Fominskaja [6]

Answer:

1/16 of the cereal is in each bowl

Step-by-step explanation:

5 1

2 years ago

Read 3 more answers

0.75(4x + 2) = 5 - (x + 1.5)<br> X =

djverab [1.8K]